Accurate frequency estimation of short-duration signals is crucial in many modern applications, including radar systems, biomedical signal analysis, and structural health monitoring. The Discrete Fourier Transform (DFT), which is the standard tool for frequency estimation, is inadequate when processing short signals due to the large frequency resolution. Therefore, one frequently obtains inaccuracy in the representation of frequencies and amplitudes in the spectra. Applying the interpolation algorithm proposed by Jain improves the frequency estimation by offering sub-bin accuracy. However, it is still inefficient for short signals. We observed that the results of interpolating using Jain’s algorithm led to an overestimation of the frequency values, which is very high for specific signal lengths. This overestimation exhibits a pattern that is repeatedly observed when shortening the signal. This paper proposes enhancements to the classical Jain interpolation algorithm to improve its performance. The enhancement is performed in two steps. First, we select the proper points for interpolation to reduce the significant errors. Afterward, we find the average error for all cycles and calculate a correction term. Applied to the estimates obtained with the original Jain algorithm, we significantly reduce frequency estimation errors. The tests involving generated sinusoidal signals with various durations, in the absence and presence of noise, have shown the proposed method’s robustness and reliability.

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Enhancing the Accuracy of the Jain Interpolation Algorithm for Short Signal Frequency Estimation

  • Daniela Giorgiana Burtea,
  • Gilbert-Rainer Gillich,
  • Laurentiu Garban

摘要

Accurate frequency estimation of short-duration signals is crucial in many modern applications, including radar systems, biomedical signal analysis, and structural health monitoring. The Discrete Fourier Transform (DFT), which is the standard tool for frequency estimation, is inadequate when processing short signals due to the large frequency resolution. Therefore, one frequently obtains inaccuracy in the representation of frequencies and amplitudes in the spectra. Applying the interpolation algorithm proposed by Jain improves the frequency estimation by offering sub-bin accuracy. However, it is still inefficient for short signals. We observed that the results of interpolating using Jain’s algorithm led to an overestimation of the frequency values, which is very high for specific signal lengths. This overestimation exhibits a pattern that is repeatedly observed when shortening the signal. This paper proposes enhancements to the classical Jain interpolation algorithm to improve its performance. The enhancement is performed in two steps. First, we select the proper points for interpolation to reduce the significant errors. Afterward, we find the average error for all cycles and calculate a correction term. Applied to the estimates obtained with the original Jain algorithm, we significantly reduce frequency estimation errors. The tests involving generated sinusoidal signals with various durations, in the absence and presence of noise, have shown the proposed method’s robustness and reliability.